Problem: Rewrite the equation by completing the square. $x^{2} +11 x +24 = 0$ $(x + $
Answer: $\begin{aligned} x^2 +11 x +24&=0 \\\\ x^2 +11 x&=-24 \end{aligned}$ Now we want to complete $x^2 +11 x$ into a perfect square. To do that, we should add $\left(\dfrac{{11}}{2}\right)^2={\dfrac{121}{4}}$ to it: $x^2{+11}x + {\dfrac{121}{4}}=\left(x +\dfrac{11}{2} \right)^2$ $\begin{aligned} x^2 +11 x&=-24 \\\\ x^2 +11 x + {\dfrac{121}{4}}&=-24 + {\dfrac{121}{4}} \\\\ \left(x +\dfrac{11}{2} \right)^2&=\dfrac{25}{4} \end{aligned}$ In conclusion, the equation after completing the square is written as: $\left(x +\dfrac{11}{2} \right)^2=\dfrac{25}{4}$